Stability analysis of cosmological models through Lyapunov's method

Charters, T.; Nunes, Ana; Mimoso, José P.

doi:10.1088/0264-9381/18/9/307

Cited by 25 publications

(22 citation statements)

References 27 publications

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“…One can also find some instability results, see e.g. Brauer & Nohel (1989), however, these have hardly been applied so far in the context of cosmology, see Charters et al (2001) for one such example.…”

Section: Lyapunov's Methodsmentioning

confidence: 99%

Dynamical systems applied to cosmology: Dark energy and modified gravity

et al. 2018

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The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades there has been a huge theoretical and observational effort into improving our understanding of the Universe. The cosmological equations describing the dynamics of a homogeneous and isotropic Universe are systems of ordinary differential equations, and one of the most elegant ways these can be investigated is by casting them into the form of dynamical systems. This allows the use of powerful analytical and numerical methods to gain a quantitative understanding of the cosmological dynamics derived by the models under study. In this review we apply these techniques to cosmology. We begin with a brief introduction to dynamical systems, fixed points, linear stability theory, Lyapunov stability, centre manifold theory and more advanced topics relating to the global structure of the solutions. Using this machinery we then analyse a large number of cosmological models and show how the stability conditions allow them to be tightly constrained and even ruled out on purely theoretical grounds. We are also able to identify those models which deserve further in depth investigation through comparison with observational data. This review is a comprehensive and detailed study of dynamical systems applications to cosmological models focusing on the late-time behaviour of our Universe, and in particular on its accelerated expansion. In self contained sections we present a large number of models ranging from canonical and non-canonical scalar fields, interacting models and non-scalar field models through to modified gravity scenarios. Selected models are discussed in detail and interpreted in the context of late-time cosmology.

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Section: Lyapunov's Methodsmentioning

confidence: 99%

Dynamical systems applied to cosmology: Dark energy and modified gravity

et al. 2018

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“…The dynamical stability of the cosmological model can be performed by calculating the adiabatic speed of sound through the cosmic fluid, C 2 s = dp∕d𝜌. [57][58][59][60] The model can be termed as stable or unstable, when C 2 s > 0 or C 2 s < 0 respectively. Using eqns.…”

Section: Dynamical Stability Of the Modelmentioning

confidence: 99%

Bouncing Cosmology in Extended Gravity and Its Reconstruction as Dark Energy Model

Agrawal

Tello‐Ortiz

Mishra

et al. 2021

Fortschritte der Physik

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In this paper, we have presented a bouncing cosmological model of the Universe in an extended theory of gravity. The dynamical behaviour of the model obtained from the flat FLRW space-time along with the violation of null energy condition have been shown. The geometrical parameters show singularity behaviour at the bouncing epoch. The parameters involved in the scale factor play a major role in the bouncing behaviour. In addition, the coupling parameter that resulted in the minimal matter-geometry coupling in the extended gravity has significant role to avoid the singularity of equation of state parameter at the bouncing epoch. Using a linear homogeneous perturbation calculation, we show the dynamical stability of the model.

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“…In [93] it was investigated the properties of cosmological models based on the HL gravity by using the dynamical system approach but using different normalization procedures in comparison with [41]. Lyapunov method has been used in some gravitational scenarios, say [94][95][96][97][98]. In the present work we provide a complete dynamical system analysis of HL cosmology keeping the potentials arbitrary, which is a major improvement since it allows for the extraction of information that is related to the foundations of the cosmological model and not to the specific potential form.…”

Section: Introductionmentioning

confidence: 99%

Extended phase-space analysis of the Hořava–Lifshitz cosmology

León

Paliathanasis

2019

Eur. Phys. J. C

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We examine the phase space of Hořava-Lifshitz cosmology for a wide range of self-interacting potentials for the scalar field under the detailed-balance condition and without imposing it, by means of the powerful method of fdevisers. A compactification approach is performed for the exponential potential and for potentials beyond the exponential one, extending the previous findings in the literature. By using this approach it is possible to describe the finite region of the phase space and the region where the phase-space variables becomes infinity. Furthermore, we present several results concerning the stability of the de Sitter solution in Hořava-Lifshitz cosmology using Center Manifold theory. The advantages of this procedure are unveiled immediately when it is compared with the Normal Forms Calculations presented before in the literature.

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Stability analysis of cosmological models through Lyapunov's method

Cited by 25 publications

References 27 publications

Dynamical systems applied to cosmology: Dark energy and modified gravity

Dynamical systems applied to cosmology: Dark energy and modified gravity

Bouncing Cosmology in Extended Gravity and Its Reconstruction as Dark Energy Model

Extended phase-space analysis of the Hořava–Lifshitz cosmology

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